2011-02-28 CLRS Chapter24 Single-Source Shortest Paths (下) 单源点最短路径 下
2011-03-05 15:29
357 查看
24.4 Difference constraints and shortest paths
In the general linear-programming problem, we are given an m × n matrix A, an m-vector b, and an n-vector c. We wish to find a vector xof n elements that maximizes the objective functionsubject to the m constraints given by Ax ≤ b.
In a system of difference constraints, each row of the linear-programming matrix A contains one 1 and one -1, and all other entries of Aare 0. Thus, the constraints given by Ax ≤ b are a set of m difference constraints involving n unknowns, in which each constraint is a simple linear inequality of the form
xj - xi ≤ bk,
The idea is that in a system Ax ≤ b of difference constraints, the m × n linear-programming matrix A can be viewed as the transpose of an incidence matrix for a graph with n vertices and m edges.
Given a system Ax ≤ b of difference constraints, let G = (V, E) be the corresponding constraint graph. If G contains no negative-weight cycles, then
is a feasible solution for the system. If G contains a negative-weight cycle, then there is no feasible solution for the system.
相关文章推荐
- 2011-02-27 CLRS Chapter24 Single-Source Shortest Paths 单源点最短路径
- 第十三章 ALDS1_12_B:Single Source Shortest Path I 单源最短路径
- AOJ GRL_1_A: Single Source Shortest Path (Dijktra算法求单源最短路径,邻接表)
- AOJ GRL_1_B: Shortest Path - Single Source Shortest Path (Negative Edges) (Bellman-Frod算法求负圈和单源最短路径)
- 最短路径 Part I- Single source shortest path
- java 单源最短路径问题
- HDU 1874 单源最短路径
- 解题报告-HDOJ-1874(单源最短路径——Dijkstra)
- poj_1502_MPI Maelstrom(Dijkstra求单源最短路径)
- 洛谷P3371【模板】单源最短路径
- 单源最短路径-迪杰斯特拉算法(Dijkstra's algorithm)
- 图的单源最短路径Bellman-Ford算法
- HDU 2680 Choose the best route(单源最短路径)
- HDU 4522 湫湫系列故事——过年回家(单源最短路径)
- 最短路径基本介绍(2)--Dijkstra算法(单源最短路径算法)
- 贪心算法——单源最短路径 dijkstra
- 算法导论笔记:24单源最短路径
- 单源最短路径问题[Dijkstra实现]
- 单源最短路径(Dijkstra算法)
- 单源最短路径--Dijkstra